Earthquake failure sequences along a cellular fault zone in a three‐dimensional elastic solid containing asperity and nonasperity regions

Numerical simulations of earthquake failure sequences along a discrete cellular fault zone are performed for a three‐dimensional (3‐D) model representing approximately the central San Andreas fault. The model consists of an upper crust overlying a lower crust and mantle region, together defining an elastic half‐space with a vertical half‐plane fault. The fault contains a region where slip is calculated on a uniform grid of cells governed by a static/kinetic friction law and regions where slip is prescribed so as to represent tectonic loading, aseismic fault creep, and adjacent great earthquakes. The computational region models a 70‐km‐long and 17.5‐km‐deep section of the San Andreas fault to the NW of the great 1857 rupture zone. Different distributions of stress drops on failing computational cells are used to model asperity (“Parkfield asperity”) and nonasperity fault regions. The model is “inherently discrete” and corresponds to a situation in which a characteristic size of geometric disorder within the fault (i.e., cell size, here a few hundreds of meters) is much larger than the “nucleation size” (of the order of tens of centimeters to tens of meters) based on slip weakening or state evolution slip distances. The computational grid is loaded by a constant plate motion imposed at the lower crust, upper mantle, and creeping fault regions and by a “staircase” slip history imposed at the 1857 and 1906 rupture zones. Stress transfer along and outside the fault due to the imposed loadings and failure episodes along the computational grid is calculated using 3‐D elastic dislocation theory. The resulting displacement field in the computational region is compatible with geodetic and seismological observations only when the asperity and nonasperity regions are characterized by significantly different average stress drops. The frequency‐magnitude statistics of the simulated failure episodes are approximately self‐similar for small events, with b ≈ 1.2 (the b value of statistics based on rupture area b A is about 1) but are strongly enhanced with respect to self‐similarity for events larger than a critical size. This is interpreted as a direct manifestation of our 3‐D elastic stress transfer calculations; beyond certain rupture area and potency (seismic moment divided by rigidity) release values, the event is usually unstoppable, and it continues to grow to a size limited by a characteristic model dimension. This effect is not accounted for by cellular automata and block‐spring models in which the adopted simplified stress transfer laws fail to scale properly with increasing rupture size. The simulations suggest that local maxima in observed frequency‐magnitude statistics correspond to dimensions of coherent brittle zones, such as the width of the seismogenic layer or the length of a fault segment bounded by barriers. The analysis indicates that a single cell size, representing approximately a single scale of geometric disorder, cannot induce self‐similarity in a 3‐D elastic model over a broad range of magnitudes. A representation of geometric disorder covering a range of scales may thus be required to generate a wide domain of self‐similar Gutenberg‐Richter statistics. Our simulations show a great diversity in the mode of failure of the Parkfield asperity; the earthquakes themselves define an irregular sequence of events. The modeling, like many other discrete fault models, suggests that expectations for periodic Parkfield earthquakes and/or simple precursory patterns repeating from one event to the other are unrealistic.